The results challenge the notion, strongly held by some patients and advocacy groups, that Lyme disease, a bacterial infection, has a tendency to resist the usual antibiotic treatment and turn into a chronic illness that requires months or even years of antibiotic therapy.

The conclusion that new symptoms come from new infections is based on genetically fingerprinting the Lyme bacteria in people who have had the illness more than once, and finding the fingerprints don’t match.

The result means different episodes of Lyme in each patient were caused by different strains of the bacteria, and couldn’t have been relapses.

An estimated 20,000 to 30,000 cases of Lyme disease occur each year in the United States. The disease is caused by a bacterium, Borrelia burgdorferi, that is carried by deer ticks. It often begins with an expanding zone of red skin — a symptom called erythema migrans — around the tick bite, but sometimes in other areas, too. Fever, headaches, fatigue, and aches and pains often follow.

Despite research, the belief has hung on that Lyme disease bacteria can cause a chronic infection even after treatment.

Untreated, the disease can cause heart and neurological problems and arthritis, with symptoms that can come and go for years. Advanced cases that have gone months or years before being treated are most likely to result in persistent arthritis.

But when the disease is detected earlier, treatment with an antibiotic, usually two to four weeks of doxycycline, can get rid of the bacteria, according to infectious disease specialists. Even advanced cases can be cleared by the drugs, doctors say, though an extra month or so of treatment may be needed. Symptoms like pain and fatigue can linger even after the bacteria are gone, possibly because the infection caused abnormalities in the immune system.

However, some doctors, patients, and advocacy groups think that the bacteria themselves can somehow hang on despite treatment, even in cases caught early, and cause a chronic infection that requires long-term treatment with antibiotics.

In some cases, people with unexplained pain, fatigue and cognitive problems have been told they had chronic Lyme disease even though blood tests found no evidence of infection.

Several controlled studies have found that long-term antibiotics did not help people who had already been treated for Lyme disease but had such lingering problems.

Despite the data, the belief has hung on that Lyme disease bacteria can cause a chronic infection even after treatment.

The researchers who conducted the new study wanted to test that idea by finding out whether people who had repeated bouts of the disease were actually having relapses. They identified 17 patients who had erythema migrans — the rash — more than once between 1991 and 2011. Most had it twice, at least a year apart, but a few patients had it three times and one had it four times.

Many had other symptoms as well, and more than half had signs of widespread systemic infection. All were treated, and recovered fully.

Lyme bacteria were grown from skin or blood samples taken from the patients when they had the rash, and the researchers analyzed a bacterial gene that varies from one strain to another. For each patient, they compared the genes from different cases of the rash. The genotypes did not match, which the researchers said proved that each rash represented a new infection, not a relapse.

In an editorial, Dr. Allen C. Steere, a Harvard professor who was first to identify Lyme disease, said the study supported past research suggesting that new infections, not relapses, caused the new symptoms.